{"ID":2852405,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.18989","arxiv_id":"2510.18989","title":"Towards Universal Solvers: Using PGD Attack in Active Learning to Increase Generalizability of Neural Operators as Knowledge Distillation from Numerical PDE Solvers","abstract":"Nonlinear PDE solvers require fine space-time discretizations and local linearizations, leading to high memory cost and slow runtimes. Neural operators such as FNOs and DeepONets offer fast single-shot inference by learning function-to-function mappings and truncating high-frequency components, but they suffer from poor out-of-distribution (OOD) generalization, often failing on inputs outside the training distribution. We propose an adversarial teacher-student distillation framework in which a differentiable numerical solver supervises a compact neural operator while a PGD-style active sampling loop searches for worst-case inputs under smoothness and energy constraints to expand the training set. Using differentiable spectral solvers enables gradient-based adversarial search and stabilizes sample mining. Experiments on Burgers and Navier-Stokes systems demonstrate that adversarial distillation substantially improves OOD robustness while preserving the low parameter cost and fast inference of neural operators.","short_abstract":"Nonlinear PDE solvers require fine space-time discretizations and local linearizations, leading to high memory cost and slow runtimes. Neural operators such as FNOs and DeepONets offer fast single-shot inference by learning function-to-function mappings and truncating high-frequency components, but they suffer from poo...","url_abs":"https://arxiv.org/abs/2510.18989","url_pdf":"https://arxiv.org/pdf/2510.18989v1","authors":"[\"Yifei Sun\"]","published":"2025-10-21T18:13:05Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}